This paper presents a novel approach to track objects from 4D-flow MRI data. A salient feature of the proposed method is that it fully exploits the geometrical and dynamical nature of the information provided by this imaging modality. The underlying idea consists in formulating the tracking problem as a data assimilation problem, in which both position and velocity observations are extracted from the 4D-flow MRI data series. Optimal state estimation is then performed in a sequential fashion via Kalman filtering. The capabilities of the method are extensively assessed in a numerical study involving synthetic and clinical data.